Employing IMU and ArUco Marker Based Trackingto Decode the Contact Forces Exerted by Adaptive Hands

Nathan Elangovan, Anany Dwivedi, Lucas Gerez, Che-Ming Chang, and Minas Liarokapis

[7], the SDM hand [8] and the ISR-SoftHand [9] are someexamples of underactuated, adaptive prosthetic hands withcompliant joints. However, adaptive hands also suffer fromcertain shortcomings and limitations. For instance, the forcesdistribution in underactuated fingers is predetermined bytheir mechanical design and cannot be easily controlled [10].Furthermore, reconfiguration reduces the effective graspingforce at the robot fingertips during pinch grasps and couldlead to the deterioration of the grasping capabilities or tofailure to maintain the desired object positions and ori-entations. The post-contact reconfiguration experienced inadaptive fingers is commonly caused by the compliance ofthe joints, the non-rigid parts that compose their structure andthe underactuation of the mechanisms [11]. This reconfigu-ration causes the contact points between object and finger tochange until an equilibrium configuration is reached. Hencethe force exertion required to reach an equilibrium dependson the configuration of the individual phalanges, the jointcompliance, and the contact area during reconfiguration [12].Thus, there is a need to predict the actual forces exerted byadaptive hands during grasping, in order to guarantee theexecution of stable grasps.

Regarding previous works, a number of studies have triedto determine the relationship between the finger configurationand the forces exerted. Two main matrices are commonlyused to determine the effects of joint configuration on forceexertion capabilities [13]. The first is the Jacobian of thefinger that transforms the torque at each of the finger jointsto the contact force the finger generates. The second one isthe transmission matrix, that uses the types of transmissionsystems (e.g., linkages, gears, tendons) as a function todetermine the force output. In [14], the authors determine theoutput forces based on the configuration of the differentialas well as the open and closed configurations of the fingersand the thumb. In [15], the authors present a method topredict the contact forces exerted by an underactuated roboticgripper using adaptive neuro-fuzzy estimation. In [16], theauthors propose an observer based recurrent neural network(RNNOB) to estimate the non-contact forces during highlydynamic motions. In [17], authors try to reduce the post-contact reconfiguration based on a data-driven optimizationof underactuated hands.

Additional sensors such as tactile / FSR (Force SensingResistor) sensors that can provide force feedback or a flexsensor that determines the joint angles would increase thecost, the complexity and the size of the system. Moreover,the integration of force and flex sensors in adaptive hands thatuse flexure joints is extremely challenging from a cable rout-

Abstract— Adaptive, underactuated, and compliant robot hands offer a promising alternative to the fully-actuated, rigid robotic devices that are typically considered for the execution of complex tasks that require significant dexterity. The increasing popularity of adaptive hands is due to their ability to extract stable grasps even under significant object pose or other environmental uncertainties, their lightweight and affordable designs and their intuitiveness and easiness of operation. Regarding possible applications, adaptive hands have been successfully used for the execution of both robust grasping and dexterous, in-hand manipulation tasks. However, the particular class of hands also suffers from certain shortcomings and drawbacks. For example, the use of underactuation leads to a post-contact reconfiguration of the fingers that may affect the force exertion capabilities of the hands during pinch grasping. In this paper, we focus on methods to predict the contact forces exerted by adaptive hands in pinch grasps, using their post-contact reconfiguration profile. The bending profiles of the fingers are recorded using ArUco trackers and IMU sensors that are embedded on the adaptive fingers and which are used to train appropriate regression models. More precisely, we examine the efficiency of the machine learning technique (Random Forests) in predicting the exerted contact forces during the reconfiguration phase of an adaptive finger. The accuracy of the proposed method is experimentally validated for a wide range of conditions, involving different prepositionings of the robot finger with respect to the employed force sensor.

I. INTRODUCTION

Adaptive robot hands have received an increased interestover the last decade due to their simplicity and intuitivenessof operation, their cost effectiveness and their paramountefficiency in executing robust grasping and dexterous, in-hand manipulation tasks. This new class of hands uses theconcept of underactuation (less actuators than the availabledegrees of freedom) and structural compliance that allowthem to conform to the object geometry and improve theirperformance [1], [2]. In particular, adaptive robot handsoffer an increased performance in extracting stable, precisegrasps and full / power grasps, being able to efficientlyreplace complex, heavy and expensive robot hands in dif-ferent activities of daily living (ADLs) [3], [4]. Moreover,recent studies have also demonstrated their efficiency in ex-ecuting dexterous, in-hand manipulation tasks [5]. Adaptivehands have also been of key interest in the developmentof prosthetic hands owing to their increased functionalityat reduced size and weight [6]. The Open Bionics hands

Nathan Elangovan, Anany Dwivedi, Lucas Gerez, Che-Ming Chang, and Minas Liarokapis are with the New Dexterity research group, Department of Mechanical Engineering, The University of Auckland, New Zealand. E-mails: sela886@aucklanduni.ac.nz, adwi592@aucklanduni.ac.nz, lger871@aucklanduni.ac.nz, ccha425@aucklanduni.ac.nz, mi-nas.liarokapis@auckland.ac.nz

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ing perspective. Hence, in this paper we use IMU sensors thatare already used for posture recognition in adaptive handssuch as the Pisa/IIT SoftHand [18], [19] and commercialprosthetic hands such as the i-limb hand [20] and ArUcomarkers that provide a vision based estimation of the handkinematics. The data from these sensors are then processedto train a machine learning regression model.

In this paper, we exploit motion capture systems onadaptive robot hands to estimate the contact forces exertedby adaptive robot hands during fingertip / pinch graspsby taking advantage of their post-contact reconfigurationprofile. As these systems are highly nonlinear, it is difficultto obtain an accurate mathematical model to predict theforces analytically [15]. This study uses a machine learn-ing algorithm (Random Forests regression) to predict thecontact forces exerted by an adaptive robot finger (outputof the model) based on reconfiguration data (input to themodel). The reconfiguration data consists of inertial mea-surement unit (IMU) data collected from appropriate IMUsensors and vision-based data collected from a set of ArUcomarkers [21]. All markers and sensors were fixed on thedifferent phalanges of the examined adaptive robot finger.The forces exerted by the adaptive finger were measuredby a dynamometer (force sensor) unit. A wide range ofexperiments was conducted in order to validate the efficiencyof the proposed methods. During the different experimentalconditions the pose and the distance of the finger from theforce sensor was varied, as it leads to different post-contact,reconfiguration motions.

The rest of the paper is organized as follows: Section IIintroduces the force estimation methods proposed, SectionIII details the experimental setup, Section IV discusses theresults, while section V concludes the paper and discussessome possible future directions.

II. CONTACT FORCE ESTIMATION METHODS

The contact forces exerted by the adaptive robot finger areestimated based on the post-contact reconfiguration profile.This is achieved by using a machine learning algorithm(Random Forests) in order to formulate a regression problem.

In order to successfully estimate the force exerted by therobot finger, we need to solve a regression problem that mapsthe reconfiguration profile of the finger (motor current, motorposition, angle of proximal and distal phalanges w.r.t. therelaxed finger position) to the force exerted at the fingertip.We choose to use a machine learning approach becauseanalytical modelling:• does not take into account some hard to model phe-

nomena like the deformation of the fingerpads and thefriction in the finger’s tendon routing system

• depends on parameters that are hard to measure withaccuracy like the motor load and the tendon tension

For solving the regression problem, we compare theperformance of three different models: i) Multiple LinearRegression model, ii) a Support Vector Machine regressorwith Radial Basis Function (RBF) kernel, and iii) a RandomForest regressor.

Multiple Linear Regression (MLR) models the relationshipbetween two or more explanatory variables (input featurevector) and a response variable. Support Vector Machines(SVM) is a popular machine learning tool for classifica-tion and regression that was first proposed by VladimirVapnik [22]. SVM based regression is considered a non-parametric technique because it relies on kernel functions.SVM is a powerful tool, but the computational and storagerequirements increase rapidly when the dimensionality ofthe training problem increases. Random Forest (RF) is asupervised learning algorithm and was originally proposedby Tin Kam Ho of Bell Labs [23] and Leo Breiman [24]. It isan ensemble learning methods that consists of many decisiontrees and it can used for both classification and regression.The final output of the RF model is the most popular classamong all the trees in case of classification or the averageof the output of all the trees in case of regression. Since thefinal output of RF is an average of all the trees, the output isregularized and is not prone to phenomena like overfitting.

A few other advantages of a RF based learning schemeover others is that it is able work efficiently with small aswell as large databases, it is fast, and it can solve multi-dimensional problems. To create a RF model, the treesare grown using the training set. To do this, the datasetand the feature set are randomly divided by a processcalled Bootstrap Aggregation (Bagging). This is a processof random selection with replacement. Typically, 2/3 of thedataset is selected by bagging, and on this new selecteddataset Attribute Bagging is performed. Attribute Baggingis done to select ‘m’ features from the ‘M’ features of thedataset. For example, for 10 different selected values of m,10 different trees are grown. These trees are tested on theremaining 1/3 of out-of-bag data and the tree with the bestperformance is selected. The process is repeated ‘T’ differenttimes to grow ‘T’ such trees. This approach is also used tocalculate the importances of the feature variables as reportedin Fig. 5. The raw importance score for each feature variable,is computed as the average importance score of all trees ofthe RF. During the model validation phase we use the 10-fold cross validation procedure to validate all the three typeof models that we compare.

III. EXPERIMENTAL SETUP

In order to validate the efficiency of the proposed methods,we conducted two different types of experiments involvingthe collection of IMU data and vision based data of thereconfiguration profiles of the system for different experi-mental conditions. For both experiments, an anthropomor-phic, adaptive, robot finger was used. It consists of a base,a proximal phalanx, and a second link that combines themiddle and distal phalanges. The adaptive finger has twospring loaded pin joints. The joints have limited range ofoperation between 0◦ to 90◦ for θ1 and 0◦ to 90◦ for θ2. Thefinger structure consists of a combination of Polylactic Acid(PLA) plastic links and a polyurethane elastomer (urethanerubber Smooth On PMC-780) that is used on the fingerpadsto increase the friction between the finger and the object

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Fig. 1. The figure illustrates the experimental setup used for IMU-based data collection. A dynamometer was used to measure the contactforce applied by the finger, while the IMUs were used to measure theMetacarpophalangeal (MCP) and Proximal Interphalangeal (PIP) joints. Thisexperiment was conducted for 10 different finger angles from 0◦ to 90◦ in10◦ steps. The motor, the finger and the dynamometer were connected tobases that were fixed to an acrylic plate. The experiments were repeated for10 trials for every experimental condition.

during object handling, while the elastomer at the distal endof the finger acts like a distal interphalangeal joint (DIP)that has limited mobility and offers only conformability tothe object surface. The robotic finger was designed with ahlwell-known, tendon-driven actuation system for adaptiveand underactuated grippers [25]–[27].

A. IMU-based Joint Angles Data Collection

The finger was mounted onto a test structure with de-tachable mounts that allows us to vary the distance betweenthe finger and the sensor as well as the angular parame-ters. The experimental setup is shown in Fig. 1 with thedynamometer mounted with a 30◦ angle on the acrylic plate.Customized, non-conductive mounts were prepared for theIMU sensors (MPU-9250) to be attached onto the fingerstructure without interfering with the fingertips and the pha-langes reconfiguration. The Biopac MP36 data acquisitionunit (Biopac Systems, Inc., Goleta, California) was equippedwith the SS25LA dynamometer and it was used to collectthe contact force measurements. The motor (Dynamixel XM-430-W350-R) and the finger were mounted on a customacrylic plate while the dynamometer was attached onto offsetacrylic plates that had an angle different between 0◦ and90◦. The experiments were repeated for 10 trials for every

Fig. 2. The experimental setup for vision based joint angles data collection.The camera was positioned at a distance to capture the ArUco markersfor estimating the PIP and MCP joint angles of the robot finger. Thisexperiment was conducted for 10 different dynamometer (force-sensor)angles ranging from 0◦ to 90◦ in 10◦ steps. The angle change was achievedby a modular setup that allows a fast adjustment of the dynamometerangle. The experiments conducted involved 10 different trials for everyexperimental condition (dynamometer angle).

experimental condition. The IMU data, the motor positions,and the contact forces exerted on the dynamometer wererecorded from initial position of the finger through to thestop of the reconfiguration motion of the examined adaptiverobot finger. It must be noted that in certain cases it wasobserved that the finger continued to exert forces after thereconfiguration stopping point, establishing contact with thefingernail. Such trials were neglected due to the differentmaterials (fingernail is made out of tough resin) and typesof physical interaction involved and they were not includedin the examined dataset.

B. Vision-based Joint Angles Data Collection

A second optical setup was created using a 4k web cameraand a set of ArUco markers (see Fig. 2). The markers wereattached on the finger phalanges instead of the IMU sensors.ArUco is a computer vision processing library developedby Rafael Muñoz and Sergio Garrido [21] and it allows thedetection of appropriately designed square fiducial markers,providing relative positional data such as the angles andthe Cartesian coordinates for each marker. Two markerswere attached onto the finger structure (on the two differentphalanges) and the dynamometer was mounted on a pivotlocking mechanism with angular slots the orientation ofwhich could range from 0◦ to 90◦ in 10◦ steps. A pin wasused to lock the base of the dynamometer into predefined10◦ interval angles and the motor was used to actuatethe adaptive robot finger from a resting position to thesurface of the dynamometer, were forces were exerted. Themotor position, the contact forces exerted and the angularposition measurements of the adaptive robot finger jointswere recorded. The experiments were conducted for a total of10 trials for every experimental condition examined (differentangles / prepositionings of the employed dynamometer).

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Fig. 3. Comparison of IMU (left) and ArUco (right) data for MCP and PIP joint angles for the experimental condition of 30◦ dynamometer angle.

Fig. 4. The graph shows the variation of the MCP joint angle, the variation of the PIP joint angle, the variation of the actual fingertip forces measuredby the dynamometer and the RF methodology based machine learning model estimations for both ArUcos and IMUs during one experiment (for 10◦dynamometer angle).

IV. RESULTS AND DISCUSSION

Results of the IMU based and ArUco based angle mea-surements exhibit similar characteristics and trends but theArUco data had higher noise (see Fig. 3). The IMU data wasmore consistent and the measurements were able to accountfor small angle changes during finger reconfiguration. Thenoise included in the ArUco datasets was likely caused byambient lighting and occlusions or shadows created duringthe finger motion. The efficiency of the trained model wasassessed by using the percentage of the Normalized MeanSquare Error (NMSE) for accuracy, to compare the predictedand the actual object motion. The NMSE value of 0% impliesa bad fit whereas the NMSE value of 100% implies that thetwo trajectories are identical. The NMSE value is defined as,

NMSE(%) = 100∗(

1−||xr− xp||2

||xr−mean(xr)||2

), (1)

where, ||.|| indicates the 2-norm of a vector, xr is theactual reference motion and xp refers to the predicted mo-tion. Estimation results for the three models examined arepresented in Table I for all the different configurations ofthe dynamometer. The three different techniques that were

considered were MLR, RF, and SVR models. The examinedRF based models were trained with 100 trees. For the SVMregressor we used a non-linear RBF kernel. It can be notedthat the RF based models had best performance for all thedynamometer configurations for both ArUcos and IMUs.Fig. 4 compares the actual finger tip force measured withthe contact force predicted using the RF model trained withthe ArUco and IMU data. The features used for the modeltraining were, the joint angles, the motor position and themotor load (current). The Random Forests model takes intoaccount the joint angle measurements from the IMU sensorsand the ArUco markers through out the reaching, contact andpost-contact reconfiguration phases, achieving a significantaccuracy for the contact force predictions up to 96.1% forthe ArUco data and 95.3% for the IMU data.

In Fig. 5, we present the importance plots for each featurevariable for both the IMU and the ArUco based RF models,derived by the RF inherent feature variables importancecalculation procedure. It is evident that the motor positionwas overall the most important feature that was used forthe contact force prediction. The MCP and PIP joint anglesfollow in importance, while the motor load (current) was theleast important feature examined.

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TABLE IMOTION ESTIMATION RESULTS FOR DIFFERENT DYNAMOMETER ANGLES

Model Initial Angle 0◦ 10◦ 20◦ 30◦ 40◦ 50◦ 60◦ 70◦ 80◦ 90◦ Avg

ArUcoAccuracy (%) 84.9 89.9 81.0 86.9 88.2 68.8 80.7 89.3 84.8 80.2 83.5

ML

R Standard Deviation (%) 2.4 2.6 0.8 1.2 3.1 9.2 5.6 1.0 1.2 2.9 3.0

IMUAccuracy (%) 88.6 87.3 84.6 75.2 67.0 85.3 82.9 85.8 91.3 88.9 83.7

Standard Deviation (%) 3.1 2.7 6.3 22.1 9.7 5.0 5.5 2.6 1.5 8.9 6.7

ArUcoAccuracy (%) 90.9 93.4 94.8 89.8 89.7 70.3 85.3 91.1 91.9 88.0 88.5

SVM

Standard Deviation (%) 2.2 3.8 2.3 2.3 3.5 9.4 8.8 1.3 2.6 9.3 4.5

IMUAccuracy (%) 90.3 89.7 87.7 81.7 68.7 88.2 87.3 90.2 92.1 84.8 86.1

Standard Deviation (%) 3.4 3.2 5.8 10.9 16.5 5.7 5.1 2.6 2.1 8.2 6.3

ArUcoAccuracy (%) 96.1 93.9 95.4 90.1 90.4 72.6 89.8 94.6 94.7 91.2 90.8

RF Standard Deviation (%) 1.69 2.75 1.57 1.70 3.16 8.20 3.53 1.20 1.26 4.31 2.93

IMUAccuracy (%) 91.2 90.5 87.7 84.5 68.5 88.2 87.1 90.8 95.3 90.7 87.4

Standard Deviation (%) 3.67 2.96 6.35 6.74 9.66 6.41 6.55 3.07 1.01 4.66 5.10

Fig. 5. Comparison of the feature variable importances for contact force prediction based on: a) IMU data (subfigure a) and b) ArUco data (subfigure b).The importance scores are obtained using the inherent RF feature variable importance calculation procedure. The results have been normalized over theresults of the 10-fold cross-validation method.

The importance of the features are similar for the twotypes of motion capture systems. The variation of the MCPand PIP joint angles during the reaching phase, contact andpost-contact reconfiguration is presented in Fig. 4. It must benoted that the bending profile of the finger prior to establish-ing contact with the dynamometer (reaching phase) remainsconstant for all the examined experimental conditions. As thefinger approaches the object, the MCP joint angle increaseswhile the PIP joint remains unchanged until contact isestablished. Once the contact is made, the contact forceexertion begins and the force increases gradually. During thepost-contact reconfiguration phase, the distal phalanx keepsbending causing the PIP joint angle to increase while theproximal phalanx starts reconfiguring backwards decreasingthe MCP joint angle. The post contact reconfiguration ofthe finger varied widely for different angular orientationsof the dynamometer with respect to the finger base. Theforce exertion continued to increase through out the recon-figuration. Regarding the accuracies comparison, as it can

be noticed in Table I, the estimation accuracies for the RFmodel trained with the ArUco data were slightly better thanthe accuracies of the model trained with the IMU data forall the dynamometer configurations examined. This can beattributed to the high resolution of the 4K web camera usedfor the ArUco markers tracking as well as to the noise inthe ArUco training set that led to the creation of a moreefficient regression model. However the difference betweenthe ArUco and the IMU based models was marginal andfor a robust implementation IMU sensors integrated intothe finger phalanges would be more practical than ArUcomarkers that suffer from calibration, occlusion and lightingcondition errors. Furthermore, the ArUco markers require anexternal camera that needs to be positioned with a significantoffset from the robot hand, making the setup bulkier andimposing new collision constraints in cases that the gripperis attached on a robot arm. The IMU sensors on the otherhand can be integrated into the finger phalanges by designwithout restricting the motion of the system.

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V. CONCLUSIONS AND FUTURE DIRECTIONS

In this paper, we proposed a methodology that combinesRandom Forest regression models and motion capture sys-tems to predict the contact forces exerted by an adaptiverobot finger in pinch grasps, using its post-contact reconfigu-ration profile. Three different type of models were compared:i) Multiple Linear Regression model, ii) a Support VectorMachine regressor with RBF kernel and iii) a Random Forestregressor. Each model was trained with either IMU or ArUcodata and the efficiency of the different models in estimatingthe exerted contact forces was compared. The experimentalvalidation was conducted for a wide range of conditionsinvolving different prepositionings of the dynamometer withrespect to the examined finger. The experimental resultsdemonstrate that the Random Forest models trained with theIMU or ArUco data can efficiently predict the robot fingercontact forces, achieving high accuracies (up to 96.1%),independently of the examined experimental condition. Thedifference in accuracy between the IMU and ArUco basedmodels is negligible. However, the IMU sensors provide amore practical implementation, as they can be integratedwithin the fingers without affecting the overall performanceof the system (imposing new collision constraints). ArUcomarkers require a camera, a camera mount and a signifi-cant offset between the camera and the finger, making thesolution much bulkier. Many adaptive hands currently useIMU sensors for posture recognition that could also beexploited to determine the contact forces without incurringfurther costs. Though the model is finger specific, it caneasily be retrained for other adaptive fingers. Regardingfuture directions, we plan to extend the models for use infive fingered adaptive robot hands and to create a completeframework for integrated systems to perform complex anddexterous tasks.

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